Submersions of hemi-slant submanifolds

In this paper, we introduce Riemannian submersions of a hemi-slant submanifold of a Kähler manifold by observing the integrability of the anti-invariant distribution of a hemi-slant submanifold and the integrability of the vertical distribution of a Riemannian submersion. Using this notion, we show that the base manifold is a Kähler manifold in the submersion of a hemi-Kaehlerian slant submanifold of an almost Hermitian manifold. We obtain an inequality between the sectional curvature of the hemi-Kaehlerian slant submanifold and the holomorphic sectional curvature of the base manifold. If this inequality becomes equality, a geometric result is given. In addition, the Ricci tensor field on the horizontal distribution along this submersion is also found.